Human-guided physics-constrained AI agents construct an auditable model of soil-plug evolution
Organizations: Institute of Ocean Engineering, Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China · Department of Civil, Environmental, and Construction Engineering, Texas Tech University, USA
Abstract
Engineering predictions require physical mechanisms to be translated consistently into equations, discretization, code, and validation, yet errors can propagate despite local checks. Artificial-intelligence (AI) agents automate scientific tasks, but coordinating and independently auditing the theory-to-solver process under physical constraints and human oversight remains unresolved. We introduce a human-in-the-loop, physics-constrained multi-agent workflow where human experts define admissible physics and modeling boundaries, while agents retrieve evidence, derive equations, implement solvers, and audit the theory-to-code chain. Applied to soil-plug evolution during suction-caisson installation, the workflow generated and audited 6 formulations in 2.9 h of agent execution once physical knowledge and inputs were prepared. Among these formulations, adding seepage-driven soil void-ratio evolution to the geometric baseline reduced mean absolute final-heave error from 58.4% to 9.0% across 14 profiles; the selected model further incorporated near-wall dilation and achieved mean absolute percentage errors of 12.4% across 9 final-state cases and 4.2% at the endpoints of 5 process histories. Beyond predictive performance, blinded replay recovered all 9 target problems, while an independent audit uncovered 5 implementation problems after 36 predefined checks had passed. Overall, this work extends multi-agent AI beyond task automation toward human-governed engineering solvers.
Figures & tables
| Version | Diagnostic question | Workflow action | Screening outcome |
|---|---|---|---|
| V1 | Can geometric displacement caused by skirt penetration alone explain plug heave? | Established a geometric baseline from solid-volume conservation and suction-caisson design relations [ 5 ] . | Produced the largest final-heave and process final-point errors among the 6 versions. |
| V2 | How does suction-driven seepage change effective stress and void ratio? | Added source-supported relations linking seepage, effective stress, and void ratio to update the soil state [ 32 , 33 , 34 ] . | Both errors decreased only slightly relative to V1. |
| V3 | How should lateral effective stress and soil rebound evolve during confined unloading? | Updated lateral and mean effective stresses using relations for earth pressure at rest, stress history, and granular-soil elasticity [ 35 , 36 , 37 ] . | Both errors decreased only modestly relative to V2. |
| V4 | Does stress-path evolution produce additional void-ratio change in dense sand? | Introduced a stress-path-dependent void-ratio update based on state-parameter and state-dependent dilatancy relations [ 34 , 38 , 39 ] . | Produced the first substantial reduction in both screening errors relative to V3. |
| V5 | Can a more compact void-ratio update improve both final-state and process-level predictions? | Tested an alternative void-ratio update under the same parameter-source rules. | Reduced the process final-point error but increased the final-heave error. |
| V6 | Can the admitted mechanisms be assembled to keep both final-state and process errors low? | Combined the audited seepage and void-ratio relations with near-wall soil dilation and consistent final-state updating [ 40 , 15 , 6 ] . | Retained a low final-heave error and achieved the lowest process final-point error; V6 was selected. |
| Version | Derivation (min) | Implementation (min) | Independent audit (min) | Total (min) | Tokens (million) | API equivalent cost (US$) |
|---|---|---|---|---|---|---|
| V1 | 4.1 | 8.5 | 6.7 | 19.3 | 2.96 | 2.03 |
| V2 | 10.8 | 17.6 | 7.4 | 35.7 | 5.14 | 3.82 |
| V3 | 6.0 | 8.6 | 7.3 | 21.9 | 8.79 | 5.57 |
| V4 | 5.8 | 21.2 | 10.5 | 37.5 | 15.44 | 8.70 |
| V5 | 6.3 | 7.5 | 7.4 | 21.2 | 18.01 | 9.72 |
| V6 | 9.4 | 19.1 | 7.3 | 35.8 | 22.72 | 12.39 |
| Audit task | Observed result | Supported conclusion |
|---|---|---|
| Blinded replay of known issues | All 9 known issues were recovered and localized; no issues outside the target set, and no human assistance was provided during the scored replay. | The retained development records enabled an isolated audit role to recover and localize known issues under blinded conditions. |
| Derivation-to-code probe audit | All 36 predefined checks passed; the separate audit reported 5 additional findings across 4 of the 5 probes, with no finding in one probe. | The role-separated audit identified both an omitted predefined rule and implementation issues not covered by the predefined checks. |
| Final code verification | All 37 code tests passed, comprising 33 module-level tests and 4 regression tests; all 5 independently calculated reference checks also passed. | Within the checked scope, the final implementation followed the equations and calculation sequence described in the manuscript. |
| Section | Content |
|---|---|
| Supplementary Note 1 | Model formulation and numerical solution procedure. |
| Supplementary Note 2 | Design and findings of the two workflow audits. |
| Supplementary Note 3 | Verification of the final solver through module-level, regression, and analytical reference tests. |
| Supplementary Note 4 | Benchmark inputs, data sources, and comparison results. |
| Supplementary Data 1 | Numerical data underlying the benchmark summaries and Fig. 5 of the main text. |
| Supplementary Data 2 | Sources and uses of the global and case-specific model inputs. |
| Symbol or mark | Definition | Unit or type |
|---|---|---|
| Geometry and coordinates | ||
| : inner caisson diameter; : outer caisson diameter; : inner caisson radius. | m | |
| : internal cross-sectional area; : outer-to-inner area ratio, . | : m 2 ; : dimensionless | |
| : penetration depth; : depth at the start of the current step; : depth at the end of the current step. | m | |
| : penetration increment; : penetration rate; : elapsed time for one step. | : m; : m s -1 ; : s | |
| : net plug heave; : total plug length; : domain height measured from the plug free surface, . | m | |
| Check | Metric | Value |
|---|---|---|
| Component combination | Mean absolute final-heave error with only | 58.42% |
| Component combination | Mean absolute final-heave error with and | 9.01% |
| Component combination | Mean absolute final-heave error with , , and | 9.48% |
| Relative heave increment | Mean absolute ratio of the heave increment to final plug heave, all profiles | 0.956% |
| Relative heave increment | Mean absolute ratio of the heave increment to final plug heave, final state prediction | 0.097% |
| Relative heave increment | Mean absolute ratio of the heave increment to final plug heave, continuous process prediction | 2.503% |
| Audit task | Materials shown to the audit role | Information not shown | Question evaluated |
|---|---|---|---|
| Blinded audit replay (A1–A9) | The relevant physical relation, calculation rule, required input and output of the code module, uncorrected code or output, and available check records | The issue label, answer key, prior discussion, correction history, and other project files | Can the audit role find and locate a known issue without being given its answer? |
| Derivation-to-code probes (P1–P5) | The supplied equations and state-update rules, generated code, and results of the fixed implementation checks | The target problem and answer | Can the audit role identify omissions or inconsistencies not covered by the predeclared checks? |
| Scored item | What was checked | Criterion for a pass |
|---|---|---|
| Finding and location | Whether the report found the target problem and named the affected equation, calculation step, or code location | The target problem and its location are both identified correctly |
| Consequence and correction | Physical or numerical consequence, proposed correction, and follow-up check | The correction addresses the problem and the follow-up check can verify it |
| False positives and human assistance | Any unrelated finding and any help given during replay | The target problem is found without an incorrect additional finding or an extra hint |
| Independent probe finding | The equation or rule that the code failed to follow, its code location, and the supporting check result | The report identifies a specific omission or disagreement from the supplied equations, code, and check results |
| Case | Target problem | What the audit role had to check |
|---|---|---|
| A1 | Correction for near-wall soil dilation absent from the solver call chain | Whether the solver calls the correction |
| A2 | Degree-valued passed directly to a trigonometric function expecting radians | Whether the angle unit matches the function input |
| A3 | Committed local increment not limited by the remaining dilation capacity | Whether the applied increment remains within the available capacity |
| A4 | The reported mean effective stress and deviatoric stress retained their trial values and were not recalculated from the final stresses | Whether the reported mean effective stress and deviatoric stress are recalculated from the final stresses |
| A5 | Trial iterations overwrite committed history before convergence is accepted | Whether history is saved only after convergence |
| A6 | Reference confinement uses vertical trial stress instead of lateral trial stress | Which stress is used as the reference confinement |
| Probe | Calculation checked | Fixed checks passed | What the independent audit found |
|---|---|---|---|
| P1 | Recalculation of final outputs in converged, edge, and nonconverged branches | 10/10 | One branch omitted the final-output recalculation; an additional check was added |
| P2 | Active nodes and the piecewise calculation in | 11/11 | One code branch could fail, and the supplied instructions did not state clearly whether inactive grid nodes remained in the input |
| P3 | Saving history only after convergence is accepted | 5/5 | The code stopped checking trials as soon as it found one that met the convergence criterion. However, the recorded count included all supplied trials, including those that had not been checked. |
| P4 | Applying rebound before calculating the remaining capacity | 5/5 | The code and equation treated differently in the numerator |
| P5 | Recalculating hydraulic and stress outputs from the final geometry | 5/5 | All final-refresh checks were repeated and no additional problem was found |
| Test group | Number of tests | Main operations checked | Acceptance criterion and observed result | Outcome |
|---|---|---|---|---|
| Hydraulic closure and moving-boundary stress | 10 | Pressure-difference recovery, tip gradient, free-surface stress, suction-controlled boundaries, and pump-flow separation | Integral and boundary residuals remain within the adopted tolerance; pump flow does not update plug heave or void ratio | Passed |
| Bolton relationship and closure | 9 | Node activation, reference confinement, dilatancy, mobilized displacement, capacity truncation, and final clipping | The correction is non-negative, capacity-limited, and confined to active nodes | Passed |
| path update and projection constraints | 6 | Mean effective stress, lateral projection, critical-state variables, rebound, state-gap release, and clipping | Updated variables match analytical or independently evaluated values | Passed |
| State commitment and final output refresh | 8 | Separation of trial and accepted states, saving after convergence, final update, output recalculation, and saved iteration and check results | Histories are saved only from accepted states, and final outputs are recalculated from the final geometry and stresses | Passed |
| ID | Check | Quantity or comparison | Criterion and observed result | Outcome |
|---|---|---|---|---|
| R-01 | Pressure-difference closure | \mathchar 28941_{\mathchar 29047}\mathchar 4946\nolimits_{\mathchar 28720}^{\mathchar 29000}\mathchar 29033\delimiter 67273472\mathchar 29048\mathchar 24891\mathchar 29050\delimiter 84054785\,\mathchar 29028\mathchar 29048\mathchar 8704\mathchar 28673\mathchar 29045\delimiter 67273472\mathchar 29050\delimiter 84054785 | Absolute residual remains within the adopted tolerance | Passed |
| R-02 | Moving free-surface stress | Zero within numerical tolerance | Passed | |
| R-03 | Deep-limit approximation | Finite-domain seepage kernel and its exponential deep-limit form | Relative difference remains within tolerance | Passed |
| R-04 | Critical-state consistency | and | Matches independent scalar evaluation | Passed |
| R-05 | capacity truncation | No node exceeds the remaining capacity | Passed | |
| B-01 | Input-sequence consistency | Penetration depths, suction-pressure history, geometry, and soil inputs | Input arrays and parameter assignments remain unchanged | Passed |
| Case group | External-boundary basis | Adopted rule | Source class |
|---|---|---|---|
| Kim and Kim (2020) [ 16 ] | 900-mm-diameter centrifuge container at 25g and 50g | m | derived |
| Tran and Randolph (2008) [ 14 ] | 390-mm by 650-mm strongbox at 100g | m | derived |
| Tjelta (1995) [ 41 ] | Full-scale field bucket without a test-box boundary | ; no finite | direct |
| Wang et al. (2019) [ 44 ] | 1.50-m by 0.96-m by 0.90-m model box | m | derived |
| Zhao et al. (2025) [ 43 ] | 1.0-m by 0.5-m by 0.6-m model tank | m | derived |
| Setting | Adopted value or rule | Source basis | Use |
|---|---|---|---|
| 1.0 central; 0.9–1.1 band | Declared sensitivity rule | Prediction sensitivity band | |
| 0.019 | Same-form silica-sand CSL prior | State update | |
| 0.7 | Same-form silica-sand CSL prior | State update | |
| 100 kPa | Reference pressure paired with the CSL prior | State update | |
| 0.006 | Fixed global coefficient | update | |
| 0.30 | Granular-soil literature range | Lateral-stress update |
| Study | Benchmark comparison | Data obtained from the study | Use in the comparison |
|---|---|---|---|
| Koteras and Ibsen (2019) [ 42 ] | Volume closure, six tests | Geometry, penetration, final heave, and before/after void ratio are direct; area ratio is derived. | Closure uses the reported void-ratio change. |
| Ragni et al. (2020) [ 15 ] | Formula reduction, one test | Prototype geometry, penetration and heave ratios, geometric decomposition, and PIV strain are direct. | The retained test uses the reported self-weight boundary condition. |
| Kim and Kim (2020) [ 16 ] | Final state prediction, four profiles | Geometry, final heave, suction–depth curves, and most soil properties are direct; missing state inputs follow cited analog or common rules. | Digitized normalized curves are converted at prototype scale; . |
| Tran and Randolph (2008) [ 14 ] | Final state prediction, five profiles | Geometry, suction curves, and most soil properties are direct; initial state is derived where required. | Final heave is calculated as , where is the caisson length and is the final penetration depth digitized from the published curve. |
| Tjelta (1995) [ 41 ] | Full-scale process prediction, A3 | Field suction and heave are direct; soil-state inputs combine site/design information and cited regional analogs. | The solver uses ; no finite outer boundary is imposed. |
| Wang et al. (2019) [ 44 ] | Laboratory process prediction | Geometry, process curves, and the principal soil properties are direct or derived from reported values. | Case inputs use the common hydraulic-ratio and prediction sensitivity band rules in S4.2. |
| Case | Test | Measured heave (mm) | Predicted heave (mm) | Error (%) | Source basis |
|---|---|---|---|---|---|
| Koteras and Ibsen (2019) | T1 | 45.00 | 49.53 | 10.07 | Reported void-ratio closure. |
| Koteras and Ibsen (2019) | T2 | 47.00 | 48.57 | 3.33 | Reported void-ratio closure. |
| Koteras and Ibsen (2019) | T3 | 44.00 | 47.60 | 8.19 | Reported void-ratio closure. |
| Koteras and Ibsen (2019) | T4 | 42.00 | 54.40 | 29.54 | Reported void-ratio closure. |
| Koteras and Ibsen (2019) | T5 | 49.00 | 55.40 | 13.06 | Reported void-ratio closure. |
| Koteras and Ibsen (2019) | T9 | 57.00 | 58.45 | 2.55 | Reported void-ratio closure. |
| Case | Profile | Measured final heave (cm) | Central final heave (cm) | Band min (cm) | Band max (cm) | Central error (%) |
|---|---|---|---|---|---|---|
| Kim and Kim (2020) | T1-1 S 25g | 66.00 | 48.26 | 37.00 | 58.31 | -26.87 |
| Kim and Kim (2020) | T1-2 S 50g | 53.00 | 52.30 | 39.47 | 64.53 | -1.32 |
| Kim and Kim (2020) | T3-1 S 50g | 58.00 | 50.74 | 38.28 | 63.13 | -12.52 |
| Kim and Kim (2020) | T4-3 S 25g | 70.00 | 59.47 | 46.04 | 73.80 | -15.05 |
| Tran and Randolph (2008) | TRAN-T1 | 50.85 | 60.53 | 48.07 | 70.46 | 19.04 |
| Tran and Randolph (2008) | TRAN-T2 | 45.04 | 41.63 | 34.20 | 47.79 | -7.56 |
| Case | Profile | Measured final point (cm) | Central final point (cm) | Band min (cm) | Band max (cm) | Final-point error (%) |
|---|---|---|---|---|---|---|
| Tjelta (1995) | TJELTA-A3 | 15.43 | 16.70 | 14.45 | 18.98 | 8.23 |
| Wang et al. (2019) | full process | 4.79 | 4.96 | 4.51 | 5.41 | 3.45 |
| Zhao et al. (2025) | ZHAO-T1 | 3.68 | 3.73 | 3.40 | 4.06 | 1.29 |
| Zhao et al. (2025) | ZHAO-T2 | 3.48 | 3.67 | 3.37 | 3.98 | 5.49 |
| Zhao et al. (2025) | ZHAO-T3 | 3.28 | 3.37 | 3.10 | 3.63 | 2.74 |
| Case | Profile | Curve MAPE (%) | Curve RMSE (cm) | Curve NRMSE (%) |
|---|---|---|---|---|
| Tjelta (1995) | TJELTA-A3 | 95.49 | 3.15 | 20.42 |
| Wang et al. (2019) | full process | 19.24 | 0.52 | 10.80 |
| Zhao et al. (2025) | ZHAO-T1 | 36.73 | 0.16 | 4.22 |
| Zhao et al. (2025) | ZHAO-T2 | 119.25 | 0.14 | 3.92 |
| Zhao et al. (2025) | ZHAO-T3 | 13.88 | 0.14 | 4.25 |
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